Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants

•We propose a simple method to implement matrix assembly in Galerkin meshfree methods.•By looping over groups of quadrature points, performance is significantly improved.•We propose a method to efficiently store the maximum entropy basis functions.•It stores partial information, at the expense of a...

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Vydáno v:	Computers & structures Ročník 150; s. 52 - 62
Hlavní autoři:	Peco, Christian, Millán, Daniel, Rosolen, Adrian, Arroyo, Marino
Médium:	Journal Article Publikace
Jazyk:	angličtina
Vydáno:	Elsevier Ltd 01.04.2015
Témata:	74 Mechanics of deformable solids 74S Numerical methods Anàlisi numèrica Assembly Balancing Basis functions Classificació AMS Code optimization CONSTRUCTION FINITE-ELEMENT-METHOD FORMULATION FRACTURE Galerkin methods INTERPOLANTS KERNEL PARTICLE METHODS Local maximum entropy Matemàtiques i estadística Matrix structure creation Maximum entropy Meshfree methods MESHLESS METHODS Mètodes numèrics Numerical methods and algorithms Optimal memory storage PHASE-FIELD MODELS Resistència de materials SCHEMES SEAMLESS BRIDGE Sparse matrix efficient assembly Stores Strategy Àrees temàtiques de la UPC Local maximum entropy Optimal memory storage Sparse matrix efficient assembly Code optimization Meshfree methods Matrix structure creation
ISSN:	0045-7949, 1879-2243
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Shrnutí:	•We propose a simple method to implement matrix assembly in Galerkin meshfree methods.•By looping over groups of quadrature points, performance is significantly improved.•We propose a method to efficiently store the maximum entropy basis functions.•It stores partial information, at the expense of a negligible amount of extra operations. In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing basis functions can be significant in problems requiring repetitive evaluations. We show that it is possible to overcome these two bottlenecks resorting to simple and effective algorithms. First, we create and fill the matrix by coarse-graining the connectivity between quadrature points and nodes. Second, we store only partial information about the basis functions, striking a balance between storage and computation. We show the performance of these strategies in relevant problems.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0045-7949 1879-2243
DOI:	10.1016/j.compstruc.2014.12.005